People are afraid of nuclear fission whether or not those fears are justified. That is human nature and it is unlikely to change.
Nonsense. It's not even remotely human nature, and it was changed, forcibly. Humanity's fear, and in particular Americans' fear of nuclear power is one of the great propaganda victories of the 20th Century.
Immediately after the end of World War II, the Greatest Generation was absolutely convinced that they were entering the Atomic Age and that it was going to be the best thing since sliced bread. Science fiction was absolutely saturated with atomic everything, and even though it was a disrespected fringe literature at the time, that didn't stop its enthusiasm from leaking over into the rest of the world. To the point where "atomic" became synonymous with "good", "modern", and "the future", slapped on advertising copy as a matter of course, in much the same way as "green" is today. The phrase "too cheap to meter" originated in 1954, and though the speaker was referring to fusion power, the phrase stuck, and is still applied today, to both fission and fusion. (Sarcastically, nowadays, but it persists nonetheless.) The future was bright, and it was going to be nuclear powered.
Then Green Peace set themselves against it. They spent the '60s and '70s telling the world how dangerous nuclear power was, and when the Three Mile Island accident happened in 1979, they were quick to capitalize on it, despite there being zero injuries or deaths caused by it right up through the present day. They spent the next seven years hammering on that accident, trying to convince the world how scary nuclear power was. And they were succeeding. If the propaganda had gone the other way, Three Mile Island would have been a great victory for nuclear power. Even with a partial core meltdown, no one was injured. The "Big Scary Thing" had happened, and it wasn't scary at all. Except people were being told that it was scary, and after a generation of it being hammered on, it was starting to stick.
Then in 1986, the Chernobyl disaster happened, the greatest gift to anti-nuclear forces since the bombings of Hiroshima and Nagasaki. And still, it could have gone the other way. The Nixon era attempt at détente had withered and the USSR was again the Great Enemy of America. (The USSR didn't disintegrate until the tail end of 1991.) Chernobyl could have been spun as a Soviet screwup, proof of the inherent inferiority of the Soviet system and indeed, it was used for that purpose, but by far the loudest message hitched to that disaster was "nuclear bad". And it worked.
It took two generations of intense propaganda and legal obstructionism, but Green Peace won. They had completely reversed the attitude towards nuclear power of an entire continent. Meanwhile, between 1946 and 1989, 4208 people, including 116 children, died in coal mining accidents and disasters around the world, while just 31 people died as a direct result of Chernobyl. (The count of indirect deaths of both coal burning and the Chernobyl disaster are violently disputed, so I'll leave them aside, saying only that both are much bigger than the direct deaths.) Human nature should have been terrified of coal by the end of the 20th Century, because it had indisputably and directly killed so many. Human nature is to be scared of the things we're told to be scared off, and not the things that are actually numerically scary.
The fear of nuclear power is many things, but it's anything but natural.
 The number of motor vehicle deaths in the US peaked in 1972, at 54,589. Modern vehicles really are a good deal safer than they once were. Still dangerous as hell. But safer.